Entering edit mode
Hello Benjamin!
I think there is some misunderstanding here. The t-test is a test for
the differences between the means of two distributions. If you center
your data like you propose the difference is 0 so the t-statistic will
always behave very much like under the nullhypothesis (not exactly as
the distributions might differ in variances and other properties, but
the t-test is NOT meant to detect those).
The F-test on the other hand specifically tests for difference in
variances, so it is clearly the more appropriate test in your case
(and
if you are worrried about non-normality you might determine p-values
by
a resampling method like bootstrap).
I think what might have confused you is that there are TWO F-tests:
a) the one for testing differences between variances (lets call that
F1)
b) the F-test that is being used in Analysis of Variance (ANOVA) (lets
call it F2)
Despite its name ANOVA is a method to compare MEANS not VARIANCES.
With
two groups you have the trivial case of a one-way ANOVA and if you
calculate the F-statistic F2 for that it is just a transformation of
the
usual t-statistic, i.e. the test will yield the same p-values.
So F1 and F2 are very different statistics for very different things,
but both have a F-distribution under normality assumptions so their
names are the same (there are plenty of chi-square tests out there as
well!)
Hope this helps
Claus
Benjamin Otto wrote:
> Dear community,
>
>
>
> That might be a stupid statistical question but I'm really not sure
about
> the answer:
>
>
>
> Suppose I have two groups of numeric values x11-x19 and y11-y19.
The
> conventional way to check for difference in variance here is
performing an
> F-test with say
>
>
>
>> g1 <- c(x11:x19)
>
>> g2 <- c(y11:y19)
>
>> var.test( g1, g2)
>
>
>
> and looking at the resuting p.value. A second possibility is
calculating
> some adjusted values first like
>
>
>
>> g1.adj <- abs(g1 - mean(g1))
>
>> g2.adj <- abs(g2 - mean(g2))
>
>
>
> And afterwards performing a T-test on those values. Should that give
me the
> same result? I tried to solve it mathematically and the statistic
doesn't
> seem to be the same. But then, why is the F-test calculated as it is
AND is
> it really better for a comparison than the second version?
>
>
>
> Regards,
>
>
>
> benjamin
>
>
>
> --
> Benjamin Otto
> Universitaetsklinikum Eppendorf Hamburg
> Institut fuer Klinische Chemie
> Martinistrasse 52
> 20246 Hamburg
>
>
>
>
> [[alternative HTML version deleted]]
>
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>
>
--
**********************************************************************
*************
Dr Claus-D. Mayer | http://www.bioss.ac.uk
Biomathematics & Statistics Scotland | email: claus at bioss.ac.uk
Rowett Research Institute | Telephone: +44 (0) 1224
716652
Aberdeen AB21 9SB, Scotland, UK. | Fax: +44 (0) 1224 715349
